From the rules page on A/E:
...
# Faction owned capital ships that are in hyperspace are considered territory for the faction that owns them.
# Arrest is not possible aboard all other ships during hyperspace travel.
# Ships, vehicles and other entities that are docked aboard a faction owned capital ship or station is considered the territory of the faction.

Im not sure why hyperspace is listed in item 1, 2 makes it seem that ship class is immaterial and any ship in hyper effects arrest. 3 is really what Im curious about.

If Im on a faction owned Capital ship entering into enemy territory is that capital ship consider sovereign ground like a mobile faction controlled land mass?

Umm, the '..all other...' part of #2 is referring to #1 - ie you can arrest on a capital no matter what, but freighters and fighters cannot be arrested on in hyper.

And yes capital ships are considered the factions territory for purposes of A/E, so if you are in an enemy space, they cannot arrest you on your capital so long as they don't meet any of the requisites for being able to arrest.